An object is placed 11 cm in front of a convex mirror of focal length 4 cm. Using the lens equation, find where the image will form and state whether it is a real or virtual image.
See my answer to "Joe" in the question which follows yours
To find the location of the image formed by the convex mirror, we can use the lens equation:
(1/f) = (1/d₀) + (1/dᵢ)
Where:
f = focal length of the convex mirror
d₀ = distance of the object from the mirror (in this case, it is positive because the object is in front of the mirror)
dᵢ = distance of the image from the mirror (positive if the image is formed on the same side as the object, negative if it is formed on the opposite side)
Given values:
f = 4 cm (positive because it's a convex mirror)
d₀ = 11 cm (positive because the object is in front of the mirror)
To find dᵢ, we can rearrange the lens equation:
(1/dᵢ) = (1/f) - (1/d₀)
Plugging in the values:
(1/dᵢ) = (1/4) - (1/11)
To simplify this equation, we take the reciprocal of both sides:
dᵢ = 1 / [(1/4) - (1/11)]
Now, to find if the image formed is real or virtual, we check the sign of dᵢ. If dᵢ is positive, the image is virtual (formed on the same side as the object). If dᵢ is negative, the image is real (formed on the opposite side as the object).
Evaluating the equation for dᵢ:
dᵢ = 1 / [(1/4) - (1/11)]
dᵢ ≈ 14.67 cm
Since dᵢ is positive, the image formed is virtual.